标题： 可视化运动控制优化景观 显示英文标题

标题： Visualizing Movement Control Optimization Landscapes

摘要： 大量动画研究集中于运动控制的优化，无论是作为动作序列还是策略参数。然而，由于目标函数的解析表达式通常不可用，我们对这些优化问题的理解受到限制。基于最近关于分析神经网络训练的研究，我们贡献了高维控制优化景观的新可视化；这为我们提供了对为什么控制优化困难以及为什么像早期终止和基于样条的动作参数化等常见做法可以简化优化的原因的洞察。例如，我们的实验表明，随着轨迹变长，轨迹优化可能变得越来越病态，但将控制参数化为部分目标状态——例如，使用PD控制器将目标角度转换为扭矩——可以作为一种有效的预条件器。我们的可视化和定量实证数据还表明，对于长时间规划范围，神经网络策略优化比轨迹优化表现得更好。我们的工作推进了对运动优化的理解，我们的可视化也应在教育应用中提供价值。 显示英文摘要

摘要： A large body of animation research focuses on optimization of movement control, either as action sequences or policy parameters. However, as closed-form expressions of the objective functions are often not available, our understanding of the optimization problems is limited. Building on recent work on analyzing neural network training, we contribute novel visualizations of high-dimensional control optimization landscapes; this yields insights into why control optimization is hard and why common practices like early termination and spline-based action parameterizations make optimization easier. For example, our experiments show how trajectory optimization can become increasingly ill-conditioned with longer trajectories, but parameterizing control as partial target states---e.g., target angles converted to torques using a PD-controller---can act as an efficient preconditioner. Both our visualizations and quantitative empirical data also indicate that neural network policy optimization scales better than trajectory optimization for long planning horizons. Our work advances the understanding of movement optimization and our visualizations should also provide value in educational use.